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Word problem from the Līlāvatī (12th century), with its English translation and solution. In science education, a word problem is a mathematical exercise (such as in a textbook, worksheet, or exam) where significant background information on the problem is presented in ordinary language rather than in mathematical notation.
The word problem for an algebra is then to determine, given two expressions (words) involving the generators and operations, whether they represent the same element of the algebra modulo the identities. The word problems for groups and semigroups can be phrased as word problems for algebras. [1]
Therefore, it is not opposite day, but if you say it is a normal day it would be considered a normal day, which contradicts the fact that it has previously been stated that it is an opposite day. Richard's paradox : We appear to be able to use simple English to define a decimal expansion in a way that is self-contradictory.
More broadly, proof by contradiction is any form of argument that establishes a statement by arriving at a contradiction, even when the initial assumption is not the negation of the statement to be proved. In this general sense, proof by contradiction is also known as indirect proof, proof by assuming the opposite, [2] and reductio ad ...
[88] (opposite of appeal to tradition) Appeal to poverty (argumentum ad Lazarum) – supporting a conclusion because the arguer is poor (or refuting because the arguer is wealthy). (Opposite of appeal to wealth.) [89] Appeal to tradition (argumentum ad antiquitatem) – a conclusion supported solely because it has long been held to be true. [90]
One of the widely used types of impossibility proof is proof by contradiction.In this type of proof, it is shown that if a proposition, such as a solution to a particular class of equations, is assumed to hold, then via deduction two mutually contradictory things can be shown to hold, such as a number being both even and odd or both negative and positive.
The following statements are examples of false equivalence: [3] "The Deepwater Horizon oil spill is no more harmful than when your neighbor drips some oil on the ground when changing his car's oil." The "false equivalence" is the comparison between things differing by many orders of magnitude: [ 3 ] Deepwater Horizon spilled 210 million US gal ...
In category theory, a branch of mathematics, duality is a correspondence between the properties of a category C and the dual properties of the opposite category C op.Given a statement regarding the category C, by interchanging the source and target of each morphism as well as interchanging the order of composing two morphisms, a corresponding dual statement is obtained regarding the opposite ...